A186462 T(n,k)=Number of (n+1)X(k+1) binary arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

16, 21, 21, 42, 30, 42, 61, 51, 51, 61, 106, 88, 111, 88, 106, 151, 128, 162, 162, 128, 151, 245, 197, 270, 309, 270, 197, 245, 359, 292, 362, 449, 449, 362, 292, 359, 567, 457, 590, 673, 797, 673, 590, 457, 567, 840, 688, 846, 945, 1061, 1061, 945, 846, 688, 840, 1301

Offset: 1

Author

R. H. Hardin Feb 22 2011

Keywords

• nonn
• tabl

Comments

Table starts

..16...21...42...61..106..151...245...359...567...840..1301...1941...2977

..21...30...51...88..128..197...292...457...688..1058..1589...2424...3651

..42...51..111..162..270..362...590...846..1362..1998..3122...4622...7126

..61...88..162..309..449..673...945..1493..2201..3473..5177...7993..11949

.106..128..270..449..797.1061..1681..2285..3681..5281..8437..12401..19317

.151..197..362..673.1061.1693..2377..3677..5073..7977.11533..18221..26957

.245..292..590..945.1681.2377..4121..5633..8893.11977.19037..27133..43249

.359..457..846.1493.2285.3677..5633..9477.13245.20281.27573..43177..62025

.567..688.1362.2201.3681.5073..8893.13245.22933.31217.48241..64785.102213

.840.1058.1998.3473.5281.7977.11977.20281.31217.52197.71885.109497.148069

Examples

			Some solutions for 4X3
..1..0..0....1..1..0....1..0..1....1..0..1....0..1..0....1..0..1....0..0..0
..1..0..0....0..0..1....0..1..0....0..1..0....0..0..1....0..1..0....0..0..0
..0..1..0....0..0..0....1..0..1....1..0..1....0..0..0....0..0..1....0..0..0
..0..0..1....1..0..0....0..1..0....0..1..1....1..0..0....0..0..0....0..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..2449

Formula

Empirical, for every column: a(n)=2*a(n-1)-2*a(n-3)+2*a(n-4)-a(n-5) for n>max(8,k+6)